How? Let’s say a minimum wage actually does what the people who push it believe: i.e., actually increase wages without disemploying anyone. So people get more money. But where does the money come from? It’s got to come from somewhere: if it’s not coming fresh off the printing press – i.e., if the money supply isn’t being increased (“printing press” not to be taken literally; it isn’t necessary to produce more physical banknotes to increase the money supply) – then it must be taken away from somewhere else. And if it’s taken away from somewhere, some prices must fall: whatever “inflation” occurs in certain consumer goods due to the minimum wage workers being paid more must be offset by “deflation” somewhere else. But “inflation” (in the mainstream view) is defined as an overall increase in prices, not a rise in some prices and a fall in others! So there’s no inflation! Except, of course, that they actually measure inflation by choosing some particular set of prices and ignoring everything else, so it’s perfectly possible that the prices they look at can increase! (Of course they can and do change the set of prices, and/or weightings, to get whatever result they want, too)
The only way to get “inflation” in the way they define it, other than as a measurement artifact, is for the money supply to increase (i.e., “inflation” in the Austrian sense).